A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $36$ and the height of the cylinder is $8$ . If the volume of the solid is $64 pi$ , what is the area of the base of the cylinder?

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $36$ and the height of the cylinder is $8$ . If the volume of the solid is $64 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-11-16T03:42:57

20.1

Explanation:

A Conical Volume is given by:
$V = 1/3 * pi * r^2 * h$
A Cylindrical Volume is given by:
$V = pi * r^2 * h$
Circular Area (base of cylinder)
$A = 2*pi * r^2$

Total solid volume =
$64pi = 1/3 * pi * r^2 * h_1 + pi * r^2 * h_2$

Solve for r.
$64 = 1/3 * r^2 * 36 + r^2 * 8$ ; $64 = r^2 * 12 + r^2 * 8$
$64 = r^2 * 20$ ; $64/20 = r^2$ ;

$r^2$ = 3.2 ; r = 1.79

$A = 2*pi * 3.2 = 20.1$

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $36$ and the height of the cylinder is $8$ . If the volume of the solid is $64 pi$ , what is the area of the base of the cylinder?

1 Answer

Explanation:

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 36 36 and the height of the cylinder is 8 8 . If the volume of the solid is 64 pi64 pi, what is the area of the base of the cylinder?

1 Answer

Explanation:

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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $36$ and the height of the cylinder is $8$ . If the volume of the solid is $64 pi$ , what is the area of the base of the cylinder?